Triple

T11412034
Position Surface form Disambiguated ID Type / Status
Subject Methods of Representation Theory E270393 entity
Predicate covers P1393 FINISHED
Object Maschke’s theorem
Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
E924213 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Maschke’s theorem | Statement: [Methods of Representation Theory, covers, Maschke’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Maschke’s theorem
Context triple: [Methods of Representation Theory, covers, Maschke’s theorem]
  • A. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • B. Schur–Weyl duality
    Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
  • C. Jordan–Hölder theorem
    The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
  • D. Cayley–Hamilton theorem
    The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
  • E. Artin–Wedderburn theorem
    The Artin–Wedderburn theorem is a fundamental result in ring theory that classifies all semisimple rings as finite direct products of matrix rings over division rings.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Maschke’s theorem
Triple: [Methods of Representation Theory, covers, Maschke’s theorem]
Generated description
Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Maschke’s theorem
Target entity description: Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
  • A. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • B. Schur–Weyl duality
    Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
  • C. Jordan–Hölder theorem
    The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
  • D. Cayley–Hamilton theorem
    The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
  • E. Artin–Wedderburn theorem
    The Artin–Wedderburn theorem is a fundamental result in ring theory that classifies all semisimple rings as finite direct products of matrix rings over division rings.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b855f0508190a2e57ef9407ddb1a completed April 20, 2026, 5:23 a.m.
NEDg Description generation batch_69e5c28d3824819097ff84cb4e13c923 completed April 20, 2026, 6:07 a.m.
NED2 Entity disambiguation (via description) batch_69e5c451c6c88190bcbb1f54ede35d29 completed April 20, 2026, 6:14 a.m.
Created at: April 8, 2026, 9:34 p.m.